Nuprl Lemma : es-prior-fixedpoints-unequal 11,40

es:ES, X:AbsInterface(Top), f:(E(X)E(X)).
(x:E(X). f(x) c x)
 (ee':E(X).
 (e'  prior-f-fixedpoints(e))
  ((e' = f**(e E))
  ((f**(e prior-f-fixedpoints(e')))) 
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Definitions(x  l), E(X), prior-f-fixedpoints(e), f**(e), [], A, [car / cdr], ES, False, AbsInterface(A), x:AB(x), x:AB(x), l1  l2, P  Q, x:A  B(x), b, left + right, P  Q, s = t, (e < e'), e c e', {x:AB(x)} , a < b, x:AB(x), Void, Top, f(a), E, , t  T, EState(T), a:A fp B(a), Id, , strong-subtype(A;B), Type, EqDecider(T), Unit, IdLnk, EOrderAxioms(Epred?info), kindcase(ka.f(a); l,t.g(l;t) ), Knd, loc(e), kind(e), Msg(M), type List, , val-axiom(E;V;M;info;pred?;init;Trans;Choose;Send;val;time), r  s, e < e', constant_function(f;A;B), SWellFounded(R(x;y)), , pred!(e;e'), x,yt(x;y), <ab>, pred(e), first(e), xt(x), P & Q, let x,y = A in B(x;y), t.1, S  T, ||as||, A  B, , l[i], A c B, suptype(ST), e  X, last(L), ff, inr x , tt, inl x , True, case b of inl(x) => s(x) | inr(y) => t(y), if b then t else f fi , T, P  Q, P  Q, Dec(P), b | a, a ~ b, a  b, a <p b, a < b, x f y, xLP(x), (xL.P(x)), y is f*(x), r < s, q-rel(r;x), Outcome, l_disjoint(T;l1;l2), (e <loc e'), e loc e' , e<e'.P(e), ee'.P(e), e<e'P(e), ee'.P(e), e[e1,e2).P(e), e[e1,e2).P(e), e[e1,e2].P(e), e[e1,e2].P(e), e(e1,e2].P(e), SqStable(P), a =!x:TQ(x), InvFuns(A;B;f;g), Inj(A;B;f), IsEqFun(T;eq), Refl(T;x,y.E(x;y)), Sym(T;x,y.E(x;y)), Trans(T;x,y.E(x;y)), AntiSym(T;x,y.R(x;y)), Connex(T;x,y.R(x;y)), CoPrime(a,b), Ident(T;op;id), Assoc(T;op), Comm(T;op), Inverse(T;op;id;inv), BiLinear(T;pl;tm), IsBilinear(A;B;C;+a;+b;+c;f), IsAction(A;x;e;S;f), Dist1op2opLR(A;1op;2op), fun_thru_1op(A;B;opa;opb;f), FunThru2op(A;B;opa;opb;f), Cancel(T;S;op), monot(T;x,y.R(x;y);f), IsMonoid(T;op;id), IsGroup(T;op;id;inv), IsMonHom{M1,M2}(f), a  b, IsIntegDom(r), IsPrimeIdeal(R;P), f  g, {T}, s ~ t, SQType(T), t  ...$L, #$n, |g|, no_repeats(T;l), x:A.B(x), null(as), x before y  l, L1  L2
Lemmaslast-not-before, iseg is sublist, l before sublist, before last, last wf, iseg wf, null wf3, no repeats wf, es-prior-fixedpoints-no repeats, es-prior-fixedpoints-non-null, guard wf, sq stable from decidable, decidable assert, es-prior-fixedpoints-fixed, es-fix-equal-E-interface, es-fix-equal, true wf, btrue wf, bfalse wf, es-is-interface wf, es-fix-last-prior-fixedpoints, es-interface wf, strong-subtype wf, strong-subtype-self, es-fix wf, length wf1, select wf, es-prior-fixedpoints wf, event system wf, es-causl wf, es-causle wf, es-E-interface-subtype rel, es-E wf, deq wf, EOrderAxioms wf, IdLnk wf, Msg wf, unit wf, nat wf, val-axiom wf, qle wf, cless wf, bool wf, top wf, Knd wf, kindcase wf, constant function wf, assert wf, loc wf, pred! wf, strongwellfounded wf, member wf, rationals wf, Id wf, EState wf, subtype rel wf, es-prior-fixedpoints-iseg, not wf, false wf, es-E-interface wf, l member wf

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